crc 150 bridging members in a load-bearing wall

CRC 150 Bridging Members in an Exterior Load-Bearing Wall SteelSmart® System 7.0 SP2

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Verification Manual

CRC Bridging Members in an Exterior Load-Bearing Wall


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Table of Contents

1. Objective ...........................................................................................................................3

2. Modeling using SteelSmart® System ....................................................................................4

3. Check of Safety ..................................................................................................................5

3.1 Design for Axial Compressive Load ................................................................................5

3.1.1 Allowable Compressive Strength for Global Buckling ................................................5

3.1.2 Check of Safety for Axial Compression .....................................................................8

3.2 Design for Flexural Moment .........................................................................................9

3.2.1 Allowable Flexural Strength for Initiation of Yielding ................................................9

3.2.2 Check of Safety for Flexure ................................................................................... 11

3.3 Check of Combined Axial Force and Flexural Moment .................................................. 12

3.4 Design of Connections ................................................................................................ 12

4. Conclusion ....................................................................................................................... 12

5. Verification of SteelSmart® System ................................................................................... 13


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1. Objective

The objective of this verification sample is to check the safety of using Cold-Rolled Channel

(CRC150) as a typical bridging system for an exterior load-bearing wall.

This check should be based on the following parameters:

Design Code: 2012 IBC w/ AISI S100-07/ S2-10

Design Method: ASD

Design Load Combination is D + 0.75L + 0.45W

Wall height = 12 ft

Wall stud section: 600S162-33 mil, 33Ksi

Stud spacing = 24 in.

Bridging members are located @ 48 in. o.c.

Lateral bracing spacing is considered equal to the bridging members spacing

Torsional bracing spacing is considered equal to the bridging members spacing

Bridging members are anchored at 12 ft

Wind load intensity (Iw) = 34 psf

Dead load = 400 lbs

Live load = 600 lbs

Figure 1 shows the setup of the load-bearing wall studs with the CRC150 bridging members.

Figure 1 Setup of Wall Studs with CRC 150 Members


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2. Modeling using SteelSmart® System


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3. Check of Safety

3.1 Design for Axial Compressive Load

3.1.1 Allowable Compressive Strength for Global Buckling

3.1.1.1 Properties of Section

A = gross area

= 0.1296 in.2

Cw = warping constant

= 0.001038 in.6

Ix = moment of inertia about x-axis

= 0.03899 in.4

J = Saint-Venant torsional constant

= 0.0001384 in.4

Rx = radius of gyration about x-axis

= 0.5485 in.

Ry = radius of gyration about Y-axis

= 0.1449 in.

Ro = polar radius of gyration

= 0.6217 in.

= factor calculated by Equation C4.1.2-3

= 0.8329

3.1.1.2 Nominal Global Buckling Stress (Fn)

KxLx/ Rx = slenderness ratio about x-axis

= 24/0.5485 = 43.755

KyLy/ Ry = slenderness ratio about y-axis

= 24/0.1449 = 165.645

(KL/ R)gov = governing slenderness ratio

= greater of (KxLx/ Rx) and (KyLy/ Ry)

= 165.645

Fe1 = elastic flexural buckling stress

= 2gov

2

RKL

Eπ (Eq. C4.1.1-1)

= 2

2

165.645

29500π = 10.61 ksi

ex = elastic flexural buckling stress about x-axis

= 2xxx

2

RLK

Eπ (Eq. C3.1.2.1-11)

= 2

2

43.755

29500π = 152.08 ksi


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t = torsional buckling stress

=

2

2

2

1

tt

W

o LK

ECGJ

AR

(Eq. C3.1.2.1-9)

=

2

2

224

0295000.000138411300

0.62170

1 001038.

1296.

π = 41.7 ksi

Fe2 = elastic torsional or flexural-torsional buckling stress

=

tex2

textex σ4βσσσσ2β

1 (Eq. C4.1.2-1)

=

7.108.527.108.527.108.528329.

410.83294414102

1 2 = 39.4 ksi

Fe = minimum of Fe1 and Fe2

= 10.61 ksi

c = e

y

F

F (Eq. C4.1-4)

=61.10

33 = 1.763 > 1.5 (elastic buckling)

Fn = yF

c

2

877.0

(Eq. C4.1-3)

=

33764.1

877.02

= 9.3 ksi

3.1.1.3 Flat Widths of Cross-Section Elements

Considering (B) the flange width, (t) the thickness, (R) the inside bend radius at the corners, and

the rest of dimensions shown in (Figure 3); the flat widths of the elements subjected to

compressive stresses are calculated as follows:

B

A

t

R

W

W

1

2

Figure 2 Elements of the CRC 150 Section


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W1 = B – (t + R)

= 0.50 - (0.0566+0.0849) = 0.3585 in.

W2 = A – 2 (t + R)

= 1.50 - 2 (0.0566+0.0849) = 1.217 in.

3.1.1.4 Effective Area of Stud at Uniform Stress Fn = 9.30 ksi

Element (1)

Element (1) is classified as a uniformly compressed unstiffened element, thus, the plate buckling

coefficient (K) used for the calculation of the effective width of (W1) is taken in accordance with

Section B3.1 (a) AISI S100-12 as 0.43.

The effective width of (W1) can be calculated in accordance with Section B2.1 (a) AISI S100-12 as

follows:-

Fcr = 2

1

2

W

t

)

EK

2μ(112

(Eq. B2.1-5)

= 2

2

2

0.3585

0.0566

)0.3(112

295000.43

π = 285.77 ksi

= cr

n

F

F (Eq. B2.1-4)

= 285.77

9.30 = 0.18 < 0.673

be-Flange = effective width of (W1)

= W1 (Eq. B2.1-1)

= 0.3585 in.

Element (2)

Element (2) is classified as a uniformly compressed stiffened element, thus, the effective width of

(W2) is determined in accordance with Section B2.1 (a) AISI S100-12 as follows:

K = plate buckling coefficient

= 4

Fcr = 2

22

2

W

t

)μ(112

EK

π (Eq. B2.1-5)

= 2

2

2

217.1

0566.0

30112

295004

).(

π = 230.68 ksi

= cr

n

F

F (Eq. B2.1-4)

= 230.68

9.30 = 0.20 < 0.673


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be-web = effective width of (W2)

= W2 (Eq. B2.1-1)

= 1.217 in.

Effective Area

Ae = effective area of the section

= gross area = 0.1296 in2

3.1.1.5 Allowable Compressive Strength

Pn = nominal axial compression strength of the CRC 150 member for global buckling

= AeFn (Eq. C4.1-1)

= 0.1296*9.30 = 1.205 kips

Pall = allowable compression strength of the CRC 150 member for global buckling

= Pn/c

= 1.205/1.8 = 0.670 kip

3.1.2 Check of Safety for Axial Compression

Pact-stud = axial force in the wall stud for the (D + 0.75L + 0.45W) load combination

= 400 + 0.75*600 = 850 lbs = 0.85 kip

Pact-sb = axial force in a single brace

= 0.02 Pact-stud (Section B3.1 – AISI S211-07)

= 0.02*0.85 = 0.017 kip

Pact-anchorage = total axial force in the CRC member at anchorage

= 0.5 Pact-sb(L/ Stud Spacing), where L is the distance of anchorage of bridging

members

= 0.5*0.017*(12/2) = 0.051 kip < (Pall = 0.670 kip) OK


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3.2 Design for Flexural Moment

3.2.1 Allowable Flexural Strength for Initiation of Yielding

3.2.1.1 Effective Widths Calculation - Iteration #1

The effective properties of stud are calculated by loading this stud by a stress gradient (tension-

compression) which has a value of (Fy) at the top fiber of its compression flange (Figure 3).

2

1

F2

F1

F3

M

+

_

Y

F = 50 ksitop

F = 50 ksibot

c.g.0

Figure 3 Stress Distribution on Cross-Section at Initiation of Yielding – Iteration #1

Element (1)

Element (1) is classified as a uniformly compressed unstiffened element, thus, the plate buckling

coefficient (K) used for the calculation of the effective width of (W2) is taken in accordance with

Section B3.1 (a) AISI S100-12 as 0.43.

The effective width of (W1) is then calculated in accordance with Section B2.1 (a) AISI S100-12 as

follows:

Fcr = 2

1

2

W

t

)

EK

2μ(112

(Eq. B2.1-5)

= 2

2

2

0.3585

0.0566

)0.3(112

295000.43

π = 285.77 ksi

f1 = compression stress at the centerline of (W1)

= y

cgo

cgoF

YD

0.5tYD

= 3375.05.1

2/0566.075.05.1

= 31.75 ksi

= crF

f1 (Eq. B2.1-4)

= 285.77

31.75 = 0.333 < 0.673


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be-Flange = effective width of (W1)

= W1 (Eq. B2.1-1)

= 0.3585 in.

Element (2)

Element (2) is classified as a stiffened element under stress gradient (compression-

compression), thus, the plate buckling coefficient (K) used for the calculation of the effective

width of (W2) is calculated in accordance with Section B2.3 (a) AISI S100-12 as follows:

f1 = compression stress at the upper end of (W2)

= ycgo

cgoF

Y

RtY

= 3375.0

0849.00566.075.0

= 26.774 ksi

f2 = tension stress at the lower end of (W2)

= - ycgo

cgoF

YD

RtYD

= - 3375.05.1

0849.00566.075.05.1

= -26.774 ksi

= |f2/ f1| (Eq. B2.3-1)

= |-26.774/26.744| = 1

K = 4 + 2(1 + )3 + 2(1 + ) (Eq. B2.3-2)

= 4 + 2(1 + 1)3 + 2(1 + 1) = 24.0

The effective width of (W2) is then calculated in accordance with Section B2.1 (a) AISI S100-12 as

follows:-

Fcr = 2

22

2

W

t

)μ(112

EK

π (Eq. B2.1-5)

= 22

1.217

0.0566

)0.3-(112

2950024

2

= 1384.083 ksi

= cr

1

F

f (Eq. B2.1-4)

= 1384.083

26.774 = 0.139 < 0.673

be-web = effective width of (W2) (Eq. B2.1-1)

= W2

= 1.217 in.

3.2.1.2 Effective Section Modulus

Sxe = the effective section modulus

= full section modulus = Sx

= 0.052 in.3


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3.2.1.3 Strength Increase from Cold-Work of forming

C = flangen compressio of area Total

flangen compressioin corners of Area

= tWtr

tr

mean

mean

1157.0

157.0

= 0566.0*3585.00566.0*)0566.0*5.00849.0(*157.0

0566.0*)0566.0*5.00849.0(*157.0

= 0.331

m = 0.192 (Fuv /Fyv) -0.068 (Eq. A7.2-4)

= 0.192 (45/33) – 0.068

= 0.1938

Bc = 3.69(Fuv /Fyv) -0.819(Fuv /Fyv)2 -1.79 (Eq. A7.2-3)

= 3.69 (45/33) - 0.819 (45/33)2 – 1.79

= 1.718

Fyc =

my v

c

tR

FB (Eq. A7.2-2)

=

0.1938

0.05660.0849

33718.1 = 52.44

Fya = CFyc + (1-C)Fyf (Eq. A7.2-1)

= 0.33152.44+(1-0.331)33

= 39.46 Ksi < Fuv

3.2.1.4 Allowable Flexural Strength

By reloading the section with a stress gradient having a maximum of 39.46 ksi (= Fya), the section

remained fully effective, therefore; the allowable flexural strength can be calculated as follows:

Mn = nominal flexural strength of the CRC 150 member at initiation of yielding

= SxFya (Eq. C3.1.1-1)

= 0.05239.46 = 2.05 kips.in.

Mall = allowable flexural strength of the CRC 150 member at initiation of yielding

= Mn / b

= 2.05/1.67 = 1.23 kips.in.

3.2.2 Check of Safety for Flexure

Mact = actual bending moment on the CRC member for the (D + 0.75L + 0.45W) load

combination

= 1.5 IW (S.F.) WL (S.S.) (B.S.) m (Equation D3.2.1-3, AISI S100-12)

= 1.5 (34/144000)0.4524480.6767

= 0.124 kip.in < (Mall = 1.23 kips.in.) OK


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3.3 Check of Combined Axial Force and Flexural Moment

1.0 be houldM

M

P

P

all

act

all

anchorage-act S

1.0177.01.23

0.124

0.67

0.051 Safe member

3.4 Design of Connections

Using BridgeClip (1 screw) [attached to bridging member using (1) #10 screw);

Mall-c = allowable flexural strength of clip in resisting the lateral pressure

= 0.18 kip.in.

Mact-c = required allowable flexural strength of clip in resisting the lateral pressure

= 0.124 kip.in. (See Section 3.2.2) < (Mall-c = 0.18 kip.in.) OK

Tall-c = allowable tensile strength of clip

= 0.075 kip

Tact-c = required allowable tensile strength of clip

= Pact-sb

= 0.017 kip (See Section 3.1.2) < (Tall-c = 0.075 kip) OK

(Tact-c/Tall-c) + (Mact-c/Mall-c) = (0.017/0.075) + (0.124/0.18) = 0.915 < 1.0 Safe Clip

Vall-sc = allowable shear strength of the (1) #10 screw connecting the 33-mil clip to the 54-mil

bridging member (calculations not shown)

= 0.376 kip

Vact-sc = actual shear force on the (1) #10 screw connecting the clip to the bridging member

= Pact-sb

= 0.017 kip (See Section 3.1.2) < Vall-sc Safe connection of clip to bridging member

Act/All = Vact-sc/Vall-sc

= 0.017/0.376 = 0.045

4. Conclusion

It is safe to use [CRC150 member + BridgeClip (1 screw)] as a bridging system for this load-

bearing wall.


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5. Verification of SteelSmart® System

crc 150 bridging members in a load-bearing wall

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